To strengthen the security of computer systems against network intrusions and server compromises, key splitting is often applied in order to split the secret state of the system (typically a key) into a number of (typically randomly chosen) “partial states,” or shares, which are then dispersed into a number of devices. Then, an attacker's task is much harder: Leakage of the full secret state requires that the attacker gets access to a sufficiently large number of the shares.
Recently, U.S. patent application Ser. No. 14/672,507, filed May 30, 2015 (now U.S. Pat. No. 9,813,243, issued on Nov. 7, 2017), entitled “Methods and Apparatus for Password-Based Secret Sharing Scheme,” incorporated by reference herein, disclosed password-based secret sharing (PBSS) for threshold and exclusive OR (XOR)-based secret sharing. The disclosed PBSS techniques allow for one or more of these shares to be fixed (e.g., to take predetermined values that are independent of the split key and not necessarily randomly chosen). PBSS, in particular, enables key splitting to employ a user's password or other personal secret information as a share into which the key is split, as described in the key-splitting framework disclosed in U.S. patent application Ser. No. 14/577,206, filed Dec. 19, 2014 (now U.S. Pat. No. 9,455,968, issued on Sep. 27, 2016), entitled “Protection of a Secret on a Mobile Device Using a Secret-Splitting Technique with a Fixed User Share,” incorporated by reference herein.
Nonetheless, a need remains for password-based secret sharing schemes for richer classes of sharing schemes (beyond, for example, Shamir's threshold scheme or XOR-based secret sharing).